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Use the properties of exponential and logarithmic functions to solve each system. Check your answers.

BlackZzzverrR [31]

The solved logarithmic function is 2x - y = e and x + y = 8 for log (2x - y) = 1 and log (x + y) = 3 log 2 respectively.

What is a logarithmic and exponential function?

Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet, e. For example log 10 = 1 and e^2.

Solving the given expressions: log (2x - y) = 1 and log (x + y) = 3 log 2

Applying given properties of logarithmic and exponential function;

log a + log b = log (ab)

4 log x = log x⁴

e^(log x) = 1

e^(x + y) = (e^x) × (e^y)

Take expression, log (2x - y) = 1

Applying exponential on both sides, we get,

e^(log 2x - y) = e^1

2x - y = e

To Check Results,

Taking logarithm both sides,

log (2x - y) = log e

log (2x - y) = 1

Thus, the answer is verified.

Take expression, log (x + y) = 3 log 2

Applying exponential on both sides, we get,

e^(log (x + y) = e^(3 log 2)

x + y = e^(log 8)

x + y = 8

To Check Results,

Taking logarithm both sides,

log (x + y) = log 8

log (x + y) = 3 log 2

Thus, the answer is verified.

Hence, the solved expression is 2x - y = e and x + y = 8 for log (2x - y) = 1 and log (x + y) = 3 log 2 respectively.

To learn more about the logarithmic and exponential functions, visit here:

brainly.com/question/13473114

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3 0

1 year ago

Solve division problem around answer to nearest hundredth 9.2 / 52.063

kifflom [539]

The nearest hundredth would be 0.17

8 0

3 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Oduvanchick [21]

Answer:

see attached

Step-by-step explanation:

The Pythagorean theorem can be used to find the hypotenuse associated with each pair of legs. That tells you ...

c² = a² +b² . . . . . legs a, b; hypotenuse c

__

<h3>alternate form of Pythagorean theorem</h3>

For the purpose of this problem, it is convenient to consider a slightly different form of the equation.

For legs √a and √b, the hypotenuse √c is given by ...

(√c)² = (√a)² +(√b)²

c = a +b

That is ...

legs √a, √b ⇒ hypotenuse √(a+b)

__

<h3>application to this problem</h3>

Since the legs are (mostly) given in terms of square roots, the value under the radical for the hypotenuse is simply the sum of those:

legs: √1, √2 ⇒ hypotenuse √(1+2) = √3

legs: √2, √3 ⇒ hypotenuse √(2+3) = √5

legs: √5, √3 ⇒ hypotenuse √(5+3) = √8

legs: √5, √1 ⇒ hypotenuse √(5+1) = √6

_____

<em>Additional comment</em>

You may not see the leg lengths given as square roots very often. This is a rather unusual set of problems for hypotenuse length.

6 0

1 year ago

Read 2 more answers

Jessica, Kareem, and Lamar served a total of 64 orders Monday at the school cafeteria. Jessica served 8 fewer orders than Lamar.

sergey [27]

Answer:

Jessica: 10 orders

Lamar: 18 orders

Kareem: 36 orders

Step-by-step explanation:

Let's first designate each person with a letter.

The number of orders served by Jessica can be designated as $J$

The number of orders served by Kareem can be designated as $K$

The number of orders served by Lamar can be designated as $L$

We know that they all served a total of 64 orders. This can be expressed as the sum of their orders equaling 64.

$J+K+L=64$

We also know that Jessica served 8 fewer orders than Lamar. This can be expressed as the number of orders served by Jessica, $J$ , being equal to Lamar's orders $L$ minus 8.

$J = L-8$

Fianlly, we know that Kareem served twice as many orders as Lamar. This can be expressed as the number of order's served by Kareem, $K$ , being 2 times Lamar's orders $L$ .

$K = 2L$